Metric characterizations of dimension for separable metric spaces

Authors:
Ludvik Janos and Harold Martin

Journal:
Proc. Amer. Math. Soc. **70** (1978), 209-212

MSC:
Primary 54F45

DOI:
https://doi.org/10.1090/S0002-9939-1978-0474229-9

MathSciNet review:
0474229

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Abstract: A subset *B* of a metric space (*X, d*) is called a *d*-bisector set iff there are distinct points *x* and *y* in *X* with . It is shown that if *X* is a separable metrizable space, then iff *X* has an admissible metric *d* for which whenever *B* is a *d*-bisector set. For separable metrizable spaces, another characterization of *n*-dimensionality is given as well as a metric dependent characterization of zero dimensionality.

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0474229-9

Keywords:
Bisector set,
star rigid metric,
strongly rigid metric

Article copyright:
© Copyright 1978
American Mathematical Society